Detect paragraph element change with JQuery

change events won’t fire on the paragraph. What you need are known as Mutation Observers. Here is the relevant MDN documentation. They have pretty good browser penetration; for older IEs, you can probably use the deprecated Mutation Events, though those are known to be performance killers, so be very careful. I’ll rewrite your example using Mutation Observers; you can also check out a jsFiddle demo:

$(function(){
    //Store the test paragraph node
    var test = $('#test');

    //Function to change the paragraph
    var changeParagraph = function () {
        var d = new Date();
        var time = d.getHours() + ":" + d.getMinutes() + ":" + d.getSeconds();
        test.text(time);
    };

    //Bind the paragraph changing event
    $('#submit1').on('click', changeParagraph);

    //Observe the paragraph
    this.observer = new MutationObserver( function(mutations) {
        alert('Paragraph changed!')
    }.bind(this));
    this.observer.observe(test.get(0), {characterData: true, childList: true});
});